Comment on the calculation of forces for multibody interatomic potentials

The system of particles interacting via multibody interatomic potential of general form is considered. Possible variants of partition of the total force acting on a single particle into pair contributions are discussed. Two definitions for the force acting between a pair of particles are compared. The forces coincide only if the particles interact via pair or embedded-atom potentials. However in literature both definitions are used in order to determine Cauchy stress tensor. A simplest example of the linear pure shear of perfect square lattice is analyzed. It is shown that, Hardy's definition for the stress tensor gives different results depending on the radius of localization function. The differences strongly depend on the way of the force definition.Comment: 9 pages, 2 figure

Vector-based model of elastic bonds for DEM simulation of solids

A new model for computer simulation of solids, composed of bonded rigid body particles, is proposed. Vectors rigidly connected with particles are used for description of deformation of a single bond. The expression for potential energy of the bond and corresponding expressions for forces and moments are proposed. Formulas, connecting parameters of the model with longitudinal, shear, bending and torsional stiffnesses of the bond, are derived. It is shown that the model allows to describe any values of the bond stiffnesses exactly. Two different calibration procedures depending on bond length/thickness ratio are proposed. It is shown that parameters of model can be chosen so that under small deformations the bond is equivalent to either Bernoulli-Euler rod or Timoshenko rod or short cylinder connecting particles. Simple expressions, connecting parameters of V-model with geometrical and mechanical characteristics of the bond, are derived. Computer simulation of dynamical buckling of the straight discrete rod and half-spherical shell is carried out.Comment: 11 pages, 6 figure

ФІНАНСОВЕ ЗАБЕЗПЕЧЕННЯ ФІСКАЛЬНОГО ПРОСТОРУ МІСЦЕВОГО САМОВРЯДУВАННЯ

If you need full access to the book, please write an email to the Publisher. Your request will be redirected to the author. If s/he is interested, s/he will directly contact you using the email address you have specified to discuss the conditions for obtaining access without the intermediary of the Publisher. The theoretical foundations of the study of fiscal space, the evolutionary trends of fiscal decentralization are presented. Theoretical, methodological and conceptual foundations of the formation of the fiscal space of local self-government, methodological support for the expansion of the fiscal growth. Recommended for scientists, students of institutions of higher economic education. Recommended for researchers and practitioners studying the problems of the fiscal space of local government, teachers, graduate students and students of economic specialties of higher educational institutions. Indexing:         Якщо Вам необхідно отримати повний доступ до книги, напишіть електронного листа Видавцю. Ваш запит буде переадресовано автору. У разі його зацікавленості, він безпосередньо зв'яжеться з Вами за вказаною Вами адресою електронної пошти для обговорення умов на отримання доступу без посередництва Видавця. Подано теоретичні основи дослідження фіскального простору, еволюційні тенденції фіскальної децентралізації. Теоертико-методологічні та концептуальні засади формування фіскального простору місцевого самоврядування, методичне забезпечення розширення фіскального ростору. Рекомендовано для науковців, студентів закладів вищої економічної освіти.Рекомендовано для наукових і практичних працівників, які досліджують проблеми фіскального простору місцевого самоврядування, викладачів, аспірантів і студентів економічних спеціальностей вищих навчальних закладів. Індексація:        &nbsp

Mathematical Modeling of the “Bone-Fixator” System during the Treatment of Intertrochanteric Fractures

Relevance — the need for an objective justification in choosing the type of fixation in the treatment patients with pertrochanteric hip fractures.Objective — to study the changes in the properties of a consolidating trochanteric fracture fixed by a dynamic cephalomedullary nail when subjected to cyclic dynamic loads.Materials and methods. A mathematical model was developed for trochanteric fracture of the femur (A1 according to AO classification) when fixed with a dynamic cephalomedullary nail. Then, the properties of the system were studied (pressure between fragments, mechanical stress in the bone and fixation device, displacement amplitude, neck-diaphysis angle) under a virtual load of a 80 kg body at various amount of insertion of the dynamic screw (from 10 mm to 0 mm).Results. In the process of shortening the femoral neck axis by 1 cm, the stability of the ‘bone-metal fixation device’ system increases, as indicated by a decrease in the maximum amplitude of displacements in the system under load by 16.8%, a decrease in the maximum stress in the fixation elements by 20.2%, a decrease in pressure at the site of contact of fragments by 19.8%. In addition, there was a decrease in the neck-diaphysis angle by 2.8%.Conclusion. The mathematical modeling of the ‘bone-metal fixation device’ system simulating conditions of dynamic osteosynthesis showed that there is a potential increase in the stability of the cephalomedullary system and that favorable conditions are created for the consolidation of the fracture when subjected to cyclic load of body mass

Position-Sensitive Measurements of a Single-Mode Laser Beam Spot Using the Dividing Plate Method

New position-sensitive experimental results have been obtained using the Dividing Plates method to detect the displacement of a single-mode laser beam spot of various diameters. Measurements show that with this method it is possible to attain sensitivities down to 0.18 µm$^{–1}$ for a laser beam spot diameter of 8.8 µm displaced over 2.4 µm diameter zone, defined as the area where measurements non-linearities are within 1%. The achievable measurement accuracy is limited by ADC noise and corresponds to ±0.030 nm. Application of the Dividing Plates method for position-sensitive measurements allows to build a compact version of the Precision Laser Inclinometer, the Compact PLI, with reduced overall dimensions of 20 × 20 × 20 cm$^{3}$ and weight of approximatively 10 kg

Risk of thromboembolism after intraosseous implantation of metallic devices with extracellular vesicles derived from multipotent stromal cells: preliminary results

Background. New implantation methods are of great importance due to the development of endoprostheses in traumatology and orthopedics, restorative medicine and dentistry. Equally important is the early detection and description of the implant-associated complications. The aim of the study is to find and describe thrombi and emboli in the heart and lungs formed after experimental implantation of metallic devices in the peripheral part of limb using extracellular vesicles of mesenchymal stromal cells. Methods. Outbred rabbits of both genders at the age from 4 to 6 months and of weight from 3 to 4 kg underwent experimental implantation. The study enrolled 57 species in total. They were divided into two groups: 30 animals underwent implantation of metallic devices using extracellular vesicles of mesenchymal stromal cells (EV MSCs), 27 — without their use. The rabbits’ hearts and lungs were studied by light microscopy methods at different stages after integration of screw titanium implants into the proximal condyle of the tibia using EV MSCs. Results. After implantation of metallic devices into the proximal condyle of the tibia, we detected fibrin, detritus and even the red bone marrow structures (various blast forms of hematopoietic cells: megakaryocytes, cells of the erythroid and myeloid lineages) in the right cavities of the heart. In the pulmonary arteries, we also found thrombi and emboli, which either led to the obliteration of the involved vessel or to gradual lysis, not disappearing completely within 10 days of follow-up. Conclusions. After intraosseous implantation of the metallic devices, there is an embolism risk in the right atria and ventricle of the heart and the pulmonary arteries and veins due to the debris migration with the bloodstream from the surgery site. At the same time, one cannot exclude a thrombotic risk in the heart and pulmonary arteries as a reaction to the presence of detritus. It is advisable to take measures aimed at preventing both debris releasing into the bloodstream and pulmonary embolism during any implantations into the bone tissues, even of relatively small devices. Using EV MSCs to affect the implant engraftment processes has no significant effect on the severity and frequency of thromboembolic complications